Open Access
2020 The minimax learning rates of normal and Ising undirected graphical models
Luc Devroye, Abbas Mehrabian, Tommy Reddad
Electron. J. Statist. 14(1): 2338-2361 (2020). DOI: 10.1214/20-EJS1721


Let $G$ be an undirected graph with $m$ edges and $d$ vertices. We show that $d$-dimensional Ising models on $G$ can be learned from $n$ i.i.d. samples within expected total variation distance some constant factor of $\min \{1,\sqrt{(m+d)/n}\}$, and that this rate is optimal. We show that the same rate holds for the class of $d$-dimensional multivariate normal undirected graphical models with respect to $G$. We also identify the optimal rate of $\min \{1,\sqrt{m/n}\}$ for Ising models with no external magnetic field.


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Luc Devroye. Abbas Mehrabian. Tommy Reddad. "The minimax learning rates of normal and Ising undirected graphical models." Electron. J. Statist. 14 (1) 2338 - 2361, 2020.


Received: 1 August 2019; Published: 2020
First available in Project Euclid: 26 June 2020

zbMATH: 07235713
MathSciNet: MR4116727
Digital Object Identifier: 10.1214/20-EJS1721

Primary: 62G07
Secondary: 82B20

Keywords: Density estimation , distribution learning , Fano’s lemma , Graphical model , Ising model , Markov random field , multivariate normal

Vol.14 • No. 1 • 2020
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